George Picton Barnes, 68, former head of an insurance agency in Fairfax and a noted horseman, died Friday at Commonwealth Doctors Hospital in Fairfax. He had emphysema.

Mr. Barnes, who was known to his friends as "Tee," was born in what is now Fairfax City and grew up there. In the 1930s, he trained horses in New York state for hunting, show jumping and steeplechasing.

During World War II, he enlisted in the cavalry and was transferred to tanks when the horses were phased out. He served in the 3rd Armored Division in Europe and was in action from Normandy through the Battle of the Bulge and into Germany. When he left the Army he went back to training horses in New York.

About 1950, he returned to Fairfax County where he later established an insurance business. He was president of the firm, Barnes & Phillips, at the time of his retirement in 1972. He also had been active in the real estate business in Northern Virgina. He was a former member of the Fairfax Board of Zoning appeals.

He continued to raise, train and sell horses at his property in Oakton. He had been a successful steeplechase and point-to-point jockey and was known as a particularly graceful and skillful rider.

Mr. Barnes was chief whip of the Fairfax Hunt and held that post until his death. He was a licensed horse show judge and was a member of the Professional Horsemen's Association and the National Steeplechase and Hunt Assocation.

His marriage to the former Patricia Hoffman ended in divorce.

Survivors include two children, John Douglas Barnes of Oakton, and Holley Ann Barnes of Eutaw, Ala., and one sister, Lola Upman of Santa Rose, Calif.

The family suggests that expressions of sympathy be in the form of contributions to a charity of one's choice.